QI (2003) s13e05 Episode Script
Maths
CHEERING AND APPLAUSE Go-oo-oo-od evening, good evening, good evening, good evening, good evening, good evening, and welcome to QI, where tonight we're doing the maths and making the money.
Let's meet our mathematical masterminds.
The irrational Aisling Bea.
APPLAUSE The recurring Susan Calman.
APPLAUSE A prime example, Sandi Toksvig.
APPLAUSE And the square root of f-all, Alan Davies.
LAUGHTER AND APPLAUSE So, let's get their numbers.
Susan goes: One, two, three, four Aisling goes: Two, four, six, eight Sandi goes: # Five-seven-oh-five! # And Alan goes: CHILD: 'Two twos are six! 'Two threes are seven.
Two fours are 24.
' LAUGHTER Well done.
It's getting worse, you know.
Now, what was this man very good at doing with his fingers? This man being the man sitting down with the crown.
He kind of looks like he's doing the Macarena, but I don't think they used to do that.
Is it a card trick? Is it a "nothing up my sleeves", is it one of those? It looks like that.
AISLING: Is the man in the middle Jesus? I know that face from somewhere.
- We're in the Old Testament.
- Oh, are we? - Well The man in the middle is Daniel.
He was in a lion's den, if you remember.
He was in prison and he was released from prison because he had the ability to interpret? - Dreams.
- Dreams.
- Dreams.
And the King whose dreams he interpreted was? Happy.
LAUGHTER Asleep.
N, N, N Nestafarius.
- Nebuchadnezzar.
- Nebuchadnezzar.
- Oh, I was close.
- Yes, yes.
Nebuchadnezzar, who was king of? All things around him.
- Babylon.
- He was.
- Yes.
- And the Babylonians were very good at doing what with their fingers? Gardening.
The Hanging Gardens of Babylon.
- What's the theme, yes, no, you're right.
What's - Green-fingered.
- Babylon is - What's the theme of our show tonight? - Babylon is where - Adding up, adding up.
- Maths.
- Yeah.
- Maths.
Babylonians, I won't say they invented mathematics, exactly, but they had a counting system on their fingers which was different from ours.
How's our counting system work? One, two, three, four, five One, two, three, four, five, six, seven, eight, nine, ten.
Phew! And therefore, because of that Decimal, decimal.
We have a decimal system, based on ten.
But they have a different system, they counted on their fingers differently.
- Oh, they did the - One, two, three - They went one, two, three, four - They went the JOINTS of the fingers.
- Yeah, the joints.
- Yes.
One, two, three.
Four, five, six.
Seven, eight, nine, Ten, 11, 12.
And then they'd put their thumb up.
Put their finger up.
And so on, until they got to 60, which is five iterations of 12.
After that you'd need another person.
Yes, exactly.
Just as we would need another person after ten.
That's the point.
And they had a very successful system.
Why is that important and influential? Well, it's the hours of the day, is it? Hours of the day, But the 24 divides into more than any other number, divides by two, three, four, six, eight Oh, Alan, you're on fire! .
.
and 12.
LAUGHTER AND APPLAUSE - Yeah! Absolutely right.
- Good boy! We also have 360 Degrees.
Degrees in a full circle.
- 12 is so much more pleasing, I think.
- It is.
Well, it's factorisable, and therefore it's a much more natural way.
I've got a question.
Yeah? When you want to say to someone, just one, I just want one.
You know, across a room.
Yeah.
Get me two, get me two.
How do you do that? Do you have to go like that? If you go like that it means three, you get three of everything.
It's a very interesting question.
I'm only going to tell you this three more times.
If you were Roman, that would be five, wouldn't it.
It's very confusing.
Yeah, the Romans, that's five.
Yeah.
There you are, that's it.
Now, last night, I tossed two heads at the same time.
What are the chances? What? I don't understand, what are you doing? No, no, what? No, no.
- Yeah, no, it's fine.
- No, no, I misunderstood, I misunderstood.
It's completely fine.
Two coins at the same time? Yeah, a coin here, a coin there.
I just want to know what the odds are.
Because I'm tempted to say one in three, but I bet it's not.
Well, what KLAXON SUSAN: It's seven in 94.
No, you've got two coins, right.
Yeah.
There are four possible outcomes.
There's heads-heads.
Heads-tails.
Yeah.
Tails-tails.
- And tails-heads.
- Tails-heads.
Tails-heads.
Yeah.
Yeah.
So it's one in four.
- One in four.
- One in four.
It's one in four.
Does it have anything to do with whether you normally toss with your right hand, or toss with your left hand? That's assuming it's an equal toss.
The thing is, it's not that difficult a thing to understand mathematically, but this was given to Members of Parliament as a question, in 2012.
Did that include the Chancellor of the Exchequer? Well, there was a split on party lines.
And 77% of Labour MPs got it wrong.
Now, listen, can I, I should have said this at the beginning, I have to be very honest, I am phobic about maths.
No, I understand.
I was like you, I was also my father's a mathematician, a physicist, and I was phobic about maths.
- Yeah.
- I always said, Oh, no, I'm allergic to maths, I don't, I can't do it.
- But actually it's very beautiful, isn't it, it's really - Oh, now I love it.
- I wish one could be turned on to it.
- Yeah.
- I'm going to get turned on tonight to maths.
All right.
My thinking, Stephen, is if it's a head and a tail, that's one outcome.
Yeah.
And then a tail and a tail and a head and a head.
I'm not counting which coin does a thing.
I'm still sticking with three.
Ah, then you think it's one in three.
And you're still wrong.
On the subject of probability, I've got this, it's really interesting, it's a probability issue.
You want a pack of cards each.
- I can't catch.
- Oh, well caught.
Well held.
We've got some for you.
All right.
I want you to take the cards out and give them a good shuffle, good shuffle.
I'm going to do the same.
I've just shuffled them.
Beautifully done.
Sandi's, Sandi's, Sandi's been doing it, look her, she's like a croupier.
Jesus! Yeah.
Very good.
Oh, no.
Very good.
- Yes, I've shuffled, I've riffle shuffled.
- Yeah.
- I'm not a gambler.
- OK.
OK, so can you shove your cards in here? Oh, all right, then.
All right.
Thank you.
I'll give it a good shake.
Is this going to be one of those Derren Brown ones where we all can't eat for a week, or something like that? No, nothing like that.
There you are.
There you go.
All right.
It's just about probability, it's not a big deal.
Is there anything you can't turn your hand to, Stephen? Now it's magic.
You haven't seen me turn my hand to anything yet.
OK.
And I'll put my cards in as well.
There we go.
All right.
And give it all a good shake.
All right, so you take one card out.
Don't look, and if you can put it close to your chest, but not, no, no, don't look.
I've looked, I know what it is.
Well, it doesn't matter.
All right.
The point is to shove it close to your chest so that that's where you're going to That's not your chest, darling.
The reason to shove it close to your chest is so that when you reveal it, it's camera height.
- Oh, right.
- That's all it is.
All right.
So take one out, feel it, yeah, random.
All right.
- Magic.
- Yeah, very good, very good.
All right.
I'll do the same.
All right.
All right.
I'll do the same.
OK, so the point is it's about probability.
The first card you choose, it could be anything.
And the second card, the probability it's going to be the same card is quite small.
And it's even less likely that three cards will be the same, and so on and so on.
The chances that you'd get all the cards the same is about one in two billion.
Now there is a possibility, but a very unlikely possibility, that two of the cards will be the same.
- OK.
- So Sandi, you'll reveal your card.
- Yours is the six of clubs, all right.
- Me? OK, and you reveal yours.
Oh, my God! Oh! Now Alan.
Oh! You reveal yours.
Oh, no, surely not.
No, oh, my God! And mine as well! Oh, there you go! APPLAUSE Funny, how can that happen? There it is.
- Burn him! - He's a witch.
Yeah.
There you are.
OK.
- He's a witch.
- That's a very good trick.
- Thank you very much.
That's very good.
- That's terribly good.
- All right, there we are.
- Fantastic, honestly.
- That was really good.
- Oh, you're sweet, thank you.
It was like Paul Daniels was in the room.
If only he was in the bag.
LAUGHTER So the chances were about one in two billion that you'd get all the cards the same and it just happened, this evening.
I'm amazed.
So, tell me now, do animals count? Do you mean in life, in a sort of sociological? - They count very much, in that sense.
- They count.
But do they count in the sense of actually? Well, from what I know, there are some animals that can count.
Yes, you're right.
- They all lined up for Noah.
I'm just saying.
- Yeah.
Yeah, and that's a fact story, a true fact story.
- That's a fact story, so - Yeah.
- You don't hear them fighting.
Have you any thoughts on this side of the room? Well, I can imagine a monkey can count.
Surely.
There must be a rhesus monkey with an accountancy degree, - there must be.
- Yeah.
But you're spot on.
Not only monkeys, but monkeys certainly are.
Apparently chicks when they hatch, can show some propensity towards being able to count.
One, two, three, four, five, chicks.
Because you can see their heads counting, can't you, they're like one, two, three, four.
Well, let me give you a list of some of the animals that have been spotted counting.
Pigeons, parrots, raccoons, ferrets, rats, salamanders, honeybees, monkeys and apes.
Have all been seen to count, add and subtract.
Rhesus monkeys - funny you should mention them, at Columbia University, have shown they can arrange up to nine objects in the correct numerical sequence.
It's always rhesus monkeys.
Do you not feel sorry for them? - They're always saying, oh, let's teach them to speak French, or - Yeah, you're right.
Crows and parrots can count up to five or six.
Cormorants can count up to seven.
Now how do you know that? They take seven fish back to the nest.
Not quite that.
Something like that.
Actually, Chinese fishermen have trained them to catch fish for them.
And what they do is they put a ring round their throat, so that they can't swallow fish themselves.
So they catch the fish, but dump them on the deck of the boat.
And how they've trained them is, that once they get past seven, on the eighth they get rid of the ring and the cormorant can catch its own.
I love that, when they make up their own mind.
There used to be a bear at Regent's Park Zoo in the 1920s that was fed biscuits by the general public.
And on Mondays it was half price and so they got a lot more biscuits.
And so on Tuesdays the bear used to take day the off.
Yes, that's it.
He counted days, or she, counted days - ursine calendar.
It's brilliant.
But I suppose it's when in need, like you wouldn't be needing to count up stuff if you're a bear, like, you're not But sometimes you'll see, maybe they need to count how many kids they have.
Yes, yeah.
And they can tell if one of them has gone missing.
Although ducks are rubbish at that, they are.
I lived on a house boat for many, many years, and we were forever trying to get baby ducks to join back up with mother, who'd just gone off.
She was off down to Battersea.
Sandi, loads of your stories of what you do for entertainment are like, we used to try and convince ducks to hang out with each other I suffer from a fatal condition, Aisling, which is posh voice, no money.
LAUGHTER AND APPLAUSE That sounds absolutely awful, I would hate to have that.
Anyway, now, what do moon-starers do, and why might they call themselves that? Well, the clue would appear to be in the question.
Yeah.
It's too obvious, I'd say they watch bare arses all the time.
- Yeah.
- Well, moon-starers is an anagram of astronomers.
Yay! Points to you.
Good work! That was damn fast.
It's not an anagram, it's an aptagram.
Sorry.
- Oh! - You're right, yeah.
I'll never win, Sandi Toksvig, never! What's an aptagram, Sandi? An aptagram is an anagram that, where the word means roughly the same.
Like Apple Macintosh and laptop machines.
Yeah.
Semolina - is no meal.
Yeah.
Yes, moon-starer is an anagram of astronomer.
In what time in history was that a relevant thing? The idea of anagrams and astronomers? Well, it must have been around the time of Galileo, surely.
It was indeed, the early 17th century.
But he wouldn't have spoken English, so why would he have changed his name to moon-starer? Yeah, this is an example of an anagram.
He Oh! He didn't use English anagrams, he used.
.
? GreeLatin.
Latin, very good.
There he is.
Why would they have used ars magna, great art, in that? - Oh, and that's moon is the ars.
- And ars magna is? - And then magna is - Is an anagram of anagrams.
ALL: Oh.
- So, yes.
But anyway, why - Well, because the Church took - a dim view of Not because of the Church, although the Church did take a dim view of what he did.
I like his very casual approach to the telescope.
- He's just sort of - Yeah.
Now I'm going to have a cigarette and now I'm going to look again.
Was it just to make the whole thing more fun? If only it was that.
In fact, even in his day, there was scientific rivalry.
So if you discovered something and you wanted to tell a friend about it and you didn't want anyone else to intercept the news, you gave it in anagram form.
Oh, it's like codes at school.
Yes, it is.
Exactly that, yeah.
Do you think they ever used to like rub around the telescope with ink and then run away and then he'll go, "Oh, what's that? "Oh, no, my eye! Oh, that's trickery.
" Who was his great rival and friend? Is it an anagram? I'm going to say Copernicus.
No, no, it wasn't Copernicus.
It was Kepler.
And he sent him an anagram because he had discovered the rings of Saturn in 1610.
ALAN CHORTLES No, not Saturn, that's Uranus! Oh, yeah.
Sorry, I'm laughing at the wrong one.
- It's not the right planet, but it's still funny.
- I knew one of them was funny.
And he sent Kepler this.
- Oh, my! - Ah, "smaismrm" Oh.
Yeah.
Yes.
- "Nugttauriras" - Great.
Stick that where the sun don't shine.
It's pretty obvious what he's putting there.
Yeah.
It's a Latin phrase, it actually is an anagram I have discovered the rings of Saturn.
Yes, it is that.
Altissimum planetam tergeminum observavi.
OK.
"I have observed the highest planet to be triplets.
" - Seen it.
- I know.
Does he mean he's seen the moons of it, or something? What does he mean by triplets? He thought they were moons, but in fact we now know them to be rings.
That must have been so exciting.
Do you not think? It must have been so thrilling, just that one moment when that suddenly has happened and nobody else has seen it.
I think it's quite clever, but they worked out they're planets because they were moving across the sky and the stars weren't.
I think it was just the first thing that made them think something was afoot.
Oh, I know, and that's what That one's moved.
Why has that star moved? It's not a star, it's Jupiter.
Yeah.
And planet is from the Greek for wanderer, it means a wanderer.
Oh.
They do this thing, I don't know if they're still doing it, but they did it for a long time, once a month in Reykjavik, the government would turn out all the street lighting and there would be a lecture on the public radio about the stars.
- And people would go outside.
- Oh, brilliant.
And they got rid of all the ambient light and you could look up and listen to the lecture - about what you were looking at.
Do you not think that would be a wonderful thing? - That is brilliant.
- Yeah.
- Yeah, I love that.
But in terms of anagrams, this isn't an anagram, it's actually a limerick composed by someone, which I invite you to recite to me.
See if you can.
Uh? Yes.
That's a shock, isn't it? - Yes.
- And you can do it.
- Can you? Yes.
- Yep.
- Yes, you can, it is a limerick.
- OK.
OK.
- Right.
You have to ask yourself what these number are, in fact.
They have some other A dozen and 12 dozen.
Ah! Yeah, 12, but 144 is also called a.
.
? A gross.
So a dozen, a gross, a score, plus three times the square root of four SUSAN LAUGHS HYSTERICALLY .
.
divided by seven.
You're all right, you're doing well.
Plus five.
Well, calm down.
I might have to slap you.
Yes! Are you all right? The episode of QI where Stephen just slaps me.
So say it again as a limerick.
- You can do it now.
- OK.
Yes, yes.
- Go on.
- Go on, then Susan.
A dozen, a gross and a score, plus three times the square root of four, divided by seven plus five times 11 equals nine squared plus not a bit more.
There you are.
Well done.
APPLAUSE It was a guy called Leigh Mercer who came up with that.
And it's rather good.
12 plus one equals, 11 plus two? Yes.
It does.
Yeah, but in what other ways does 12 plus one equals 11 plus two? Oh, is it an anagram, then? They're anagrams of each other.
"Twelve plus one", written out, is an anagram of "eleven plus two".
Eleven plus two.
Wow, you really have had too much time on your hands.
These were worked out by Nelson Mandela on Robben Island.
I think they're rather fabulous, so there.
They are rather.
They're marvellous.
All right, OK.
Now, what's the biggest mistake anyone's ever made with a pencil? Hmm.
Oh, I say.
Oh, now, it's got to be a miscalculation or something.
Well, ah, you'd "Ah, aah" "Yeah.
Aah" MORE IMPRESSION: "Aah, aah, now, now" - Lead poisoning? Sucking on the lead? - "Steady.
" It's not a, it's not a historical miscalculation? No, it's astonishing.
It took place in New York HE GRUNTS LOUDLY .
.
in the '90s, I think it was.
- I'll tell you exactly - All right, Stephen? Is that the pencil there? Yeah.
Just testing Were you miscalculating with a pencil there, sir? I eased it in.
I eased it in and it was all fine.
Chapter four, I eased it in and it was all fine.
In 1998, there was a problem with pencils.
"Problem with pencils.
" "Problem with pencils.
" "A pencil problem," basically, yeah.
There's no reason for you to guess what it was.
It was pencils given to children.
Ah, drugs.
Was it the one Time for drugs! I know what it was they printed, for children, pencils that said "do not use drugs" on them, and when they sharpened them, eventually it said "use drugs.
" Oh, you've dropped one.
Ah.
You're right.
Very good, very good.
Here they are.
That's "hil-ah-rious".
On, they say here, "Too cool to do drugs.
" You shave it and it goes, "cool to do drugs.
" "Cool to do drugs.
" And then you shave it again and it goes, "do drugs.
" - Yes! - Do drugs.
- There you are.
It was a bit of a mistake, but well done, Sandi.
So, other mistakes include, in 1945, the Arkansas legislature accidentally repealed all their laws at once.
With a pencil? No, they had an act with the words - "All laws and parts of laws, "and particularly Act 33 of the Acts of 1941, are hereby repealed.
" They just meant the particular one, but it legally meant all their laws.
And then in 2003, the German agency responsible for TV licences sent a series of reminders to St Walpurga, to pay her licence fee.
She died in 777.
Never having paid for her licence! No.
It didn't stop them asking.
And then in the Australian Morning Bulletin, which of course is called The Bully, they said there was an error printed in a story titled Pigs Float Down The Dawson, on page by reporter Daniel Burdon, said that "more than 30,000 pigs were floating down the Dawson River.
" Actually, what the owner of the piggery said was, that "30 sows and pigs".
"We'd like to apologise for the error.
" So, now, why did a failure to sell mirrors massively improve modern media? Because you can't put a mirror on a selfie stick.
Is that it? Well, selfies, oddly enough, are rather close to it.
- A medieval version of selfies, at least.
- Medieval? We're going back to the mid-15th century.
People used to go on.
.
? Pilgrimages.
Pilgrimages.
And a pilgrimage was a visit to a holy place, where there would be Sandwiches.
There would be sandwiches, but what were you going to see? - Some kind of shrine or something.
- Shrine, a shrine, relics.
- Shrine.
Oh, relics.
Relics.
- I love a good relic.
Bones, material, bits of beard, bits of body, bits of the true cross, bits of all kinds of stuff.
- Porn.
- Yeah.
And they were so popular that you might go there and you couldn't even get close to it.
So you'd hold up a selfie stick, as it were.
It wouldn't be a selfie stick.
It would be a box with a lid and the lid was a mirror.
And the mirror would see the relic.
And the beams and the rays would hit the mirror and go down into the box and you'd close the box and you'd go home and it contained the images, in your head at least, of the holy relics.
- Did it, really? - Seriously, one of the best pieces - of medieval marketing I've ever heard.
- Yeah.
Yes.
And this particular man was making mirrors.
And he made these mirrors for Aachen, and Aachen had Mary's robe from the night Jesus was born.
It had Jesus's swaddling clothes.
It had the cloth in which John the Baptist's head was wrapped, after he was decapitated.
The loincloth Jesus wore on the cross.
So this person we're talking about made mirrors for pilgrims to go to Aachen, but unfortunately he didn't sell any.
So he went back to his home town of Mainz, and in 1450, he produced something that changed the world forever.
A print, a stamp, a print version, Stephen, of what they'd see in - Print - And it was stamped.
- Postcards.
No, Sandi, that's kind of my idea.
No.
- Souvenir mugs.
- No.
He created printing.
He created the printed word.
MAN IN AUDIENCE: Johan Gutenberg.
Thank you, audience.
APPLAUSE He's Johannes Gutenberg.
In 1450, he created the Gutenberg Bible, and then other books he created.
- Oh, yes.
- It changed the world totally.
But unfortunately, the mistake was he went to basically a kind of Dragons' Den, who funded him.
He took a wine press, he converted the wine press into a letter press, to create books.
And then he had a Duncan Bannatyne character, "I'm out.
Out.
" - But his investors - "Don't like it, never take off, - I liked your mirrors better.
- "No.
I'm out.
" - Well, they, unfortunately they took all the money, the investors, the dragons took all the money.
He died destitute in 1468.
Very sad.
The most influential figure of his age, in those terms.
One of the first printers in Britain was called Wynkyn de Worde.
- Yes, he was.
- Don't you think that's so delightful? - There's a society, a Wynkyn society.
- Wynkyn society, yeah.
And then, of course, Caxton was the other great one.
But, yeah.
Before he invented the printing press, Gutenberg was a failed mirror-maker.
And so we enter the mad world of mangled misconceptions that we call General Ignorance.
And, given the show's theme, we've even spent a bit of money on a mathematical machine.
Ooh! Yeah, you'll be impressed with that.
Ooh.
It looks like a happy face that's taken a lot of drugs.
LAUGHTER - It does a bit, doesn't it? - Yeah.
- It's lovely.
- But what is it, Stephen? Well, I just want to know who first proved the theorem that this model demonstrates.
Pythagoras.
Pythagoras.
KLAXON Oh! My grandfather, who was from Hungary, always pronounced it "Peeta-goras.
" "So that at school doing the mathematics, "are you studying Peeta-goras?" And I thought this man, Peter Goras, who was Peter? No, it wasn't Peter Goras who first proved it.
Oh.
What is it? The theorem that needs to be discussed here? A squared equals B squared plus C squared.
- Yeah, yeah, it's - The sum of the two, the squared of two smaller sides.
The sum on the two squares is equal to the sum on the hypotenuse, exactly.
Yeah, that big one should go into the other two.
So you can see here, the yellow, that's the triangle.
These are its two sides.
And these are the squares of the two sides, they are literally geometrically expressed as squares, rather than just mathematically, as if that was, say, X, it's just not X squared, but it is literally the square, there.
And there's Y squared.
And it's supposedly equal to Z squared, which is the longest side, the hypotenuse.
Because here's the right angle, here.
These are not right angles, obviously.
And there's that.
How can we show they're equal? Well, there are all kinds of ways, but here's one way.
Drumroll, please.
Oh, yes.
THEY BANG THE DESKS All right, let's go.
Ooh.
Oh, that's very clever.
There it goes, pouring into the first square.
- Wow! - Expensive.
- Is it going to fill it up? - Wow.
- Shut the front door! - Oh, Well, it definitely equals X squared.
- Yes.
Does it equal Y squared as well? I need to go to the toilet.
LAUGHTER There's Y squared, it's filling up, it's filling up, it's filling up, it's full.
And there it is.
Hurray! APPLAUSE Isn't that satisfactory? Highly satisfactory.
It's the first theorem most people learn at school.
It's Pythagoras's theorem by name, but it wasn't, it was used many, many years before him - people used it to build buildings and Euclid demonstrated it before him.
But we give it the name of Pythagoras.
Who is Euclid, then? He was even before? He's the father of mathematics.
Euclid? - Oh, was he? - Yeah.
- Yeah.
- Oh, Euclid, yes.
Before him, nothing.
The greatest.
Yeah, well done to Euclid, we love Euclid.
So, let's take this model away.
Let's hear it for him.
APPLAUSE So, the time has come to tally-up the scores.
Oh, my actual, oh, my actual.
So, in first place, with a magnificent two points, it's Aisling Bee! Oh! APPLAUSE And with an earth-shattering zero, it's Sandi Toksvig.
APPLAUSE A more than respectable minus six, Susan Calman.
APPLAUSE And on his terms, really quite handsome, minus 43, Alan Davies.
APPLAUSE So, it's goodnight from Susan, Sandi, Aisling, Alan and me.
And I'll leave you with this dark observation from Joseph Stalin.
My favourite dictator.
"The people who cast the votes decide nothing.
"The people who count the votes decide everything.
" Goodnight.
CHEERING AND APPLAUSE
Let's meet our mathematical masterminds.
The irrational Aisling Bea.
APPLAUSE The recurring Susan Calman.
APPLAUSE A prime example, Sandi Toksvig.
APPLAUSE And the square root of f-all, Alan Davies.
LAUGHTER AND APPLAUSE So, let's get their numbers.
Susan goes: One, two, three, four Aisling goes: Two, four, six, eight Sandi goes: # Five-seven-oh-five! # And Alan goes: CHILD: 'Two twos are six! 'Two threes are seven.
Two fours are 24.
' LAUGHTER Well done.
It's getting worse, you know.
Now, what was this man very good at doing with his fingers? This man being the man sitting down with the crown.
He kind of looks like he's doing the Macarena, but I don't think they used to do that.
Is it a card trick? Is it a "nothing up my sleeves", is it one of those? It looks like that.
AISLING: Is the man in the middle Jesus? I know that face from somewhere.
- We're in the Old Testament.
- Oh, are we? - Well The man in the middle is Daniel.
He was in a lion's den, if you remember.
He was in prison and he was released from prison because he had the ability to interpret? - Dreams.
- Dreams.
- Dreams.
And the King whose dreams he interpreted was? Happy.
LAUGHTER Asleep.
N, N, N Nestafarius.
- Nebuchadnezzar.
- Nebuchadnezzar.
- Oh, I was close.
- Yes, yes.
Nebuchadnezzar, who was king of? All things around him.
- Babylon.
- He was.
- Yes.
- And the Babylonians were very good at doing what with their fingers? Gardening.
The Hanging Gardens of Babylon.
- What's the theme, yes, no, you're right.
What's - Green-fingered.
- Babylon is - What's the theme of our show tonight? - Babylon is where - Adding up, adding up.
- Maths.
- Yeah.
- Maths.
Babylonians, I won't say they invented mathematics, exactly, but they had a counting system on their fingers which was different from ours.
How's our counting system work? One, two, three, four, five One, two, three, four, five, six, seven, eight, nine, ten.
Phew! And therefore, because of that Decimal, decimal.
We have a decimal system, based on ten.
But they have a different system, they counted on their fingers differently.
- Oh, they did the - One, two, three - They went one, two, three, four - They went the JOINTS of the fingers.
- Yeah, the joints.
- Yes.
One, two, three.
Four, five, six.
Seven, eight, nine, Ten, 11, 12.
And then they'd put their thumb up.
Put their finger up.
And so on, until they got to 60, which is five iterations of 12.
After that you'd need another person.
Yes, exactly.
Just as we would need another person after ten.
That's the point.
And they had a very successful system.
Why is that important and influential? Well, it's the hours of the day, is it? Hours of the day, But the 24 divides into more than any other number, divides by two, three, four, six, eight Oh, Alan, you're on fire! .
.
and 12.
LAUGHTER AND APPLAUSE - Yeah! Absolutely right.
- Good boy! We also have 360 Degrees.
Degrees in a full circle.
- 12 is so much more pleasing, I think.
- It is.
Well, it's factorisable, and therefore it's a much more natural way.
I've got a question.
Yeah? When you want to say to someone, just one, I just want one.
You know, across a room.
Yeah.
Get me two, get me two.
How do you do that? Do you have to go like that? If you go like that it means three, you get three of everything.
It's a very interesting question.
I'm only going to tell you this three more times.
If you were Roman, that would be five, wouldn't it.
It's very confusing.
Yeah, the Romans, that's five.
Yeah.
There you are, that's it.
Now, last night, I tossed two heads at the same time.
What are the chances? What? I don't understand, what are you doing? No, no, what? No, no.
- Yeah, no, it's fine.
- No, no, I misunderstood, I misunderstood.
It's completely fine.
Two coins at the same time? Yeah, a coin here, a coin there.
I just want to know what the odds are.
Because I'm tempted to say one in three, but I bet it's not.
Well, what KLAXON SUSAN: It's seven in 94.
No, you've got two coins, right.
Yeah.
There are four possible outcomes.
There's heads-heads.
Heads-tails.
Yeah.
Tails-tails.
- And tails-heads.
- Tails-heads.
Tails-heads.
Yeah.
Yeah.
So it's one in four.
- One in four.
- One in four.
It's one in four.
Does it have anything to do with whether you normally toss with your right hand, or toss with your left hand? That's assuming it's an equal toss.
The thing is, it's not that difficult a thing to understand mathematically, but this was given to Members of Parliament as a question, in 2012.
Did that include the Chancellor of the Exchequer? Well, there was a split on party lines.
And 77% of Labour MPs got it wrong.
Now, listen, can I, I should have said this at the beginning, I have to be very honest, I am phobic about maths.
No, I understand.
I was like you, I was also my father's a mathematician, a physicist, and I was phobic about maths.
- Yeah.
- I always said, Oh, no, I'm allergic to maths, I don't, I can't do it.
- But actually it's very beautiful, isn't it, it's really - Oh, now I love it.
- I wish one could be turned on to it.
- Yeah.
- I'm going to get turned on tonight to maths.
All right.
My thinking, Stephen, is if it's a head and a tail, that's one outcome.
Yeah.
And then a tail and a tail and a head and a head.
I'm not counting which coin does a thing.
I'm still sticking with three.
Ah, then you think it's one in three.
And you're still wrong.
On the subject of probability, I've got this, it's really interesting, it's a probability issue.
You want a pack of cards each.
- I can't catch.
- Oh, well caught.
Well held.
We've got some for you.
All right.
I want you to take the cards out and give them a good shuffle, good shuffle.
I'm going to do the same.
I've just shuffled them.
Beautifully done.
Sandi's, Sandi's, Sandi's been doing it, look her, she's like a croupier.
Jesus! Yeah.
Very good.
Oh, no.
Very good.
- Yes, I've shuffled, I've riffle shuffled.
- Yeah.
- I'm not a gambler.
- OK.
OK, so can you shove your cards in here? Oh, all right, then.
All right.
Thank you.
I'll give it a good shake.
Is this going to be one of those Derren Brown ones where we all can't eat for a week, or something like that? No, nothing like that.
There you are.
There you go.
All right.
It's just about probability, it's not a big deal.
Is there anything you can't turn your hand to, Stephen? Now it's magic.
You haven't seen me turn my hand to anything yet.
OK.
And I'll put my cards in as well.
There we go.
All right.
And give it all a good shake.
All right, so you take one card out.
Don't look, and if you can put it close to your chest, but not, no, no, don't look.
I've looked, I know what it is.
Well, it doesn't matter.
All right.
The point is to shove it close to your chest so that that's where you're going to That's not your chest, darling.
The reason to shove it close to your chest is so that when you reveal it, it's camera height.
- Oh, right.
- That's all it is.
All right.
So take one out, feel it, yeah, random.
All right.
- Magic.
- Yeah, very good, very good.
All right.
I'll do the same.
All right.
All right.
I'll do the same.
OK, so the point is it's about probability.
The first card you choose, it could be anything.
And the second card, the probability it's going to be the same card is quite small.
And it's even less likely that three cards will be the same, and so on and so on.
The chances that you'd get all the cards the same is about one in two billion.
Now there is a possibility, but a very unlikely possibility, that two of the cards will be the same.
- OK.
- So Sandi, you'll reveal your card.
- Yours is the six of clubs, all right.
- Me? OK, and you reveal yours.
Oh, my God! Oh! Now Alan.
Oh! You reveal yours.
Oh, no, surely not.
No, oh, my God! And mine as well! Oh, there you go! APPLAUSE Funny, how can that happen? There it is.
- Burn him! - He's a witch.
Yeah.
There you are.
OK.
- He's a witch.
- That's a very good trick.
- Thank you very much.
That's very good.
- That's terribly good.
- All right, there we are.
- Fantastic, honestly.
- That was really good.
- Oh, you're sweet, thank you.
It was like Paul Daniels was in the room.
If only he was in the bag.
LAUGHTER So the chances were about one in two billion that you'd get all the cards the same and it just happened, this evening.
I'm amazed.
So, tell me now, do animals count? Do you mean in life, in a sort of sociological? - They count very much, in that sense.
- They count.
But do they count in the sense of actually? Well, from what I know, there are some animals that can count.
Yes, you're right.
- They all lined up for Noah.
I'm just saying.
- Yeah.
Yeah, and that's a fact story, a true fact story.
- That's a fact story, so - Yeah.
- You don't hear them fighting.
Have you any thoughts on this side of the room? Well, I can imagine a monkey can count.
Surely.
There must be a rhesus monkey with an accountancy degree, - there must be.
- Yeah.
But you're spot on.
Not only monkeys, but monkeys certainly are.
Apparently chicks when they hatch, can show some propensity towards being able to count.
One, two, three, four, five, chicks.
Because you can see their heads counting, can't you, they're like one, two, three, four.
Well, let me give you a list of some of the animals that have been spotted counting.
Pigeons, parrots, raccoons, ferrets, rats, salamanders, honeybees, monkeys and apes.
Have all been seen to count, add and subtract.
Rhesus monkeys - funny you should mention them, at Columbia University, have shown they can arrange up to nine objects in the correct numerical sequence.
It's always rhesus monkeys.
Do you not feel sorry for them? - They're always saying, oh, let's teach them to speak French, or - Yeah, you're right.
Crows and parrots can count up to five or six.
Cormorants can count up to seven.
Now how do you know that? They take seven fish back to the nest.
Not quite that.
Something like that.
Actually, Chinese fishermen have trained them to catch fish for them.
And what they do is they put a ring round their throat, so that they can't swallow fish themselves.
So they catch the fish, but dump them on the deck of the boat.
And how they've trained them is, that once they get past seven, on the eighth they get rid of the ring and the cormorant can catch its own.
I love that, when they make up their own mind.
There used to be a bear at Regent's Park Zoo in the 1920s that was fed biscuits by the general public.
And on Mondays it was half price and so they got a lot more biscuits.
And so on Tuesdays the bear used to take day the off.
Yes, that's it.
He counted days, or she, counted days - ursine calendar.
It's brilliant.
But I suppose it's when in need, like you wouldn't be needing to count up stuff if you're a bear, like, you're not But sometimes you'll see, maybe they need to count how many kids they have.
Yes, yeah.
And they can tell if one of them has gone missing.
Although ducks are rubbish at that, they are.
I lived on a house boat for many, many years, and we were forever trying to get baby ducks to join back up with mother, who'd just gone off.
She was off down to Battersea.
Sandi, loads of your stories of what you do for entertainment are like, we used to try and convince ducks to hang out with each other I suffer from a fatal condition, Aisling, which is posh voice, no money.
LAUGHTER AND APPLAUSE That sounds absolutely awful, I would hate to have that.
Anyway, now, what do moon-starers do, and why might they call themselves that? Well, the clue would appear to be in the question.
Yeah.
It's too obvious, I'd say they watch bare arses all the time.
- Yeah.
- Well, moon-starers is an anagram of astronomers.
Yay! Points to you.
Good work! That was damn fast.
It's not an anagram, it's an aptagram.
Sorry.
- Oh! - You're right, yeah.
I'll never win, Sandi Toksvig, never! What's an aptagram, Sandi? An aptagram is an anagram that, where the word means roughly the same.
Like Apple Macintosh and laptop machines.
Yeah.
Semolina - is no meal.
Yeah.
Yes, moon-starer is an anagram of astronomer.
In what time in history was that a relevant thing? The idea of anagrams and astronomers? Well, it must have been around the time of Galileo, surely.
It was indeed, the early 17th century.
But he wouldn't have spoken English, so why would he have changed his name to moon-starer? Yeah, this is an example of an anagram.
He Oh! He didn't use English anagrams, he used.
.
? GreeLatin.
Latin, very good.
There he is.
Why would they have used ars magna, great art, in that? - Oh, and that's moon is the ars.
- And ars magna is? - And then magna is - Is an anagram of anagrams.
ALL: Oh.
- So, yes.
But anyway, why - Well, because the Church took - a dim view of Not because of the Church, although the Church did take a dim view of what he did.
I like his very casual approach to the telescope.
- He's just sort of - Yeah.
Now I'm going to have a cigarette and now I'm going to look again.
Was it just to make the whole thing more fun? If only it was that.
In fact, even in his day, there was scientific rivalry.
So if you discovered something and you wanted to tell a friend about it and you didn't want anyone else to intercept the news, you gave it in anagram form.
Oh, it's like codes at school.
Yes, it is.
Exactly that, yeah.
Do you think they ever used to like rub around the telescope with ink and then run away and then he'll go, "Oh, what's that? "Oh, no, my eye! Oh, that's trickery.
" Who was his great rival and friend? Is it an anagram? I'm going to say Copernicus.
No, no, it wasn't Copernicus.
It was Kepler.
And he sent him an anagram because he had discovered the rings of Saturn in 1610.
ALAN CHORTLES No, not Saturn, that's Uranus! Oh, yeah.
Sorry, I'm laughing at the wrong one.
- It's not the right planet, but it's still funny.
- I knew one of them was funny.
And he sent Kepler this.
- Oh, my! - Ah, "smaismrm" Oh.
Yeah.
Yes.
- "Nugttauriras" - Great.
Stick that where the sun don't shine.
It's pretty obvious what he's putting there.
Yeah.
It's a Latin phrase, it actually is an anagram I have discovered the rings of Saturn.
Yes, it is that.
Altissimum planetam tergeminum observavi.
OK.
"I have observed the highest planet to be triplets.
" - Seen it.
- I know.
Does he mean he's seen the moons of it, or something? What does he mean by triplets? He thought they were moons, but in fact we now know them to be rings.
That must have been so exciting.
Do you not think? It must have been so thrilling, just that one moment when that suddenly has happened and nobody else has seen it.
I think it's quite clever, but they worked out they're planets because they were moving across the sky and the stars weren't.
I think it was just the first thing that made them think something was afoot.
Oh, I know, and that's what That one's moved.
Why has that star moved? It's not a star, it's Jupiter.
Yeah.
And planet is from the Greek for wanderer, it means a wanderer.
Oh.
They do this thing, I don't know if they're still doing it, but they did it for a long time, once a month in Reykjavik, the government would turn out all the street lighting and there would be a lecture on the public radio about the stars.
- And people would go outside.
- Oh, brilliant.
And they got rid of all the ambient light and you could look up and listen to the lecture - about what you were looking at.
Do you not think that would be a wonderful thing? - That is brilliant.
- Yeah.
- Yeah, I love that.
But in terms of anagrams, this isn't an anagram, it's actually a limerick composed by someone, which I invite you to recite to me.
See if you can.
Uh? Yes.
That's a shock, isn't it? - Yes.
- And you can do it.
- Can you? Yes.
- Yep.
- Yes, you can, it is a limerick.
- OK.
OK.
- Right.
You have to ask yourself what these number are, in fact.
They have some other A dozen and 12 dozen.
Ah! Yeah, 12, but 144 is also called a.
.
? A gross.
So a dozen, a gross, a score, plus three times the square root of four SUSAN LAUGHS HYSTERICALLY .
.
divided by seven.
You're all right, you're doing well.
Plus five.
Well, calm down.
I might have to slap you.
Yes! Are you all right? The episode of QI where Stephen just slaps me.
So say it again as a limerick.
- You can do it now.
- OK.
Yes, yes.
- Go on.
- Go on, then Susan.
A dozen, a gross and a score, plus three times the square root of four, divided by seven plus five times 11 equals nine squared plus not a bit more.
There you are.
Well done.
APPLAUSE It was a guy called Leigh Mercer who came up with that.
And it's rather good.
12 plus one equals, 11 plus two? Yes.
It does.
Yeah, but in what other ways does 12 plus one equals 11 plus two? Oh, is it an anagram, then? They're anagrams of each other.
"Twelve plus one", written out, is an anagram of "eleven plus two".
Eleven plus two.
Wow, you really have had too much time on your hands.
These were worked out by Nelson Mandela on Robben Island.
I think they're rather fabulous, so there.
They are rather.
They're marvellous.
All right, OK.
Now, what's the biggest mistake anyone's ever made with a pencil? Hmm.
Oh, I say.
Oh, now, it's got to be a miscalculation or something.
Well, ah, you'd "Ah, aah" "Yeah.
Aah" MORE IMPRESSION: "Aah, aah, now, now" - Lead poisoning? Sucking on the lead? - "Steady.
" It's not a, it's not a historical miscalculation? No, it's astonishing.
It took place in New York HE GRUNTS LOUDLY .
.
in the '90s, I think it was.
- I'll tell you exactly - All right, Stephen? Is that the pencil there? Yeah.
Just testing Were you miscalculating with a pencil there, sir? I eased it in.
I eased it in and it was all fine.
Chapter four, I eased it in and it was all fine.
In 1998, there was a problem with pencils.
"Problem with pencils.
" "Problem with pencils.
" "A pencil problem," basically, yeah.
There's no reason for you to guess what it was.
It was pencils given to children.
Ah, drugs.
Was it the one Time for drugs! I know what it was they printed, for children, pencils that said "do not use drugs" on them, and when they sharpened them, eventually it said "use drugs.
" Oh, you've dropped one.
Ah.
You're right.
Very good, very good.
Here they are.
That's "hil-ah-rious".
On, they say here, "Too cool to do drugs.
" You shave it and it goes, "cool to do drugs.
" "Cool to do drugs.
" And then you shave it again and it goes, "do drugs.
" - Yes! - Do drugs.
- There you are.
It was a bit of a mistake, but well done, Sandi.
So, other mistakes include, in 1945, the Arkansas legislature accidentally repealed all their laws at once.
With a pencil? No, they had an act with the words - "All laws and parts of laws, "and particularly Act 33 of the Acts of 1941, are hereby repealed.
" They just meant the particular one, but it legally meant all their laws.
And then in 2003, the German agency responsible for TV licences sent a series of reminders to St Walpurga, to pay her licence fee.
She died in 777.
Never having paid for her licence! No.
It didn't stop them asking.
And then in the Australian Morning Bulletin, which of course is called The Bully, they said there was an error printed in a story titled Pigs Float Down The Dawson, on page by reporter Daniel Burdon, said that "more than 30,000 pigs were floating down the Dawson River.
" Actually, what the owner of the piggery said was, that "30 sows and pigs".
"We'd like to apologise for the error.
" So, now, why did a failure to sell mirrors massively improve modern media? Because you can't put a mirror on a selfie stick.
Is that it? Well, selfies, oddly enough, are rather close to it.
- A medieval version of selfies, at least.
- Medieval? We're going back to the mid-15th century.
People used to go on.
.
? Pilgrimages.
Pilgrimages.
And a pilgrimage was a visit to a holy place, where there would be Sandwiches.
There would be sandwiches, but what were you going to see? - Some kind of shrine or something.
- Shrine, a shrine, relics.
- Shrine.
Oh, relics.
Relics.
- I love a good relic.
Bones, material, bits of beard, bits of body, bits of the true cross, bits of all kinds of stuff.
- Porn.
- Yeah.
And they were so popular that you might go there and you couldn't even get close to it.
So you'd hold up a selfie stick, as it were.
It wouldn't be a selfie stick.
It would be a box with a lid and the lid was a mirror.
And the mirror would see the relic.
And the beams and the rays would hit the mirror and go down into the box and you'd close the box and you'd go home and it contained the images, in your head at least, of the holy relics.
- Did it, really? - Seriously, one of the best pieces - of medieval marketing I've ever heard.
- Yeah.
Yes.
And this particular man was making mirrors.
And he made these mirrors for Aachen, and Aachen had Mary's robe from the night Jesus was born.
It had Jesus's swaddling clothes.
It had the cloth in which John the Baptist's head was wrapped, after he was decapitated.
The loincloth Jesus wore on the cross.
So this person we're talking about made mirrors for pilgrims to go to Aachen, but unfortunately he didn't sell any.
So he went back to his home town of Mainz, and in 1450, he produced something that changed the world forever.
A print, a stamp, a print version, Stephen, of what they'd see in - Print - And it was stamped.
- Postcards.
No, Sandi, that's kind of my idea.
No.
- Souvenir mugs.
- No.
He created printing.
He created the printed word.
MAN IN AUDIENCE: Johan Gutenberg.
Thank you, audience.
APPLAUSE He's Johannes Gutenberg.
In 1450, he created the Gutenberg Bible, and then other books he created.
- Oh, yes.
- It changed the world totally.
But unfortunately, the mistake was he went to basically a kind of Dragons' Den, who funded him.
He took a wine press, he converted the wine press into a letter press, to create books.
And then he had a Duncan Bannatyne character, "I'm out.
Out.
" - But his investors - "Don't like it, never take off, - I liked your mirrors better.
- "No.
I'm out.
" - Well, they, unfortunately they took all the money, the investors, the dragons took all the money.
He died destitute in 1468.
Very sad.
The most influential figure of his age, in those terms.
One of the first printers in Britain was called Wynkyn de Worde.
- Yes, he was.
- Don't you think that's so delightful? - There's a society, a Wynkyn society.
- Wynkyn society, yeah.
And then, of course, Caxton was the other great one.
But, yeah.
Before he invented the printing press, Gutenberg was a failed mirror-maker.
And so we enter the mad world of mangled misconceptions that we call General Ignorance.
And, given the show's theme, we've even spent a bit of money on a mathematical machine.
Ooh! Yeah, you'll be impressed with that.
Ooh.
It looks like a happy face that's taken a lot of drugs.
LAUGHTER - It does a bit, doesn't it? - Yeah.
- It's lovely.
- But what is it, Stephen? Well, I just want to know who first proved the theorem that this model demonstrates.
Pythagoras.
Pythagoras.
KLAXON Oh! My grandfather, who was from Hungary, always pronounced it "Peeta-goras.
" "So that at school doing the mathematics, "are you studying Peeta-goras?" And I thought this man, Peter Goras, who was Peter? No, it wasn't Peter Goras who first proved it.
Oh.
What is it? The theorem that needs to be discussed here? A squared equals B squared plus C squared.
- Yeah, yeah, it's - The sum of the two, the squared of two smaller sides.
The sum on the two squares is equal to the sum on the hypotenuse, exactly.
Yeah, that big one should go into the other two.
So you can see here, the yellow, that's the triangle.
These are its two sides.
And these are the squares of the two sides, they are literally geometrically expressed as squares, rather than just mathematically, as if that was, say, X, it's just not X squared, but it is literally the square, there.
And there's Y squared.
And it's supposedly equal to Z squared, which is the longest side, the hypotenuse.
Because here's the right angle, here.
These are not right angles, obviously.
And there's that.
How can we show they're equal? Well, there are all kinds of ways, but here's one way.
Drumroll, please.
Oh, yes.
THEY BANG THE DESKS All right, let's go.
Ooh.
Oh, that's very clever.
There it goes, pouring into the first square.
- Wow! - Expensive.
- Is it going to fill it up? - Wow.
- Shut the front door! - Oh, Well, it definitely equals X squared.
- Yes.
Does it equal Y squared as well? I need to go to the toilet.
LAUGHTER There's Y squared, it's filling up, it's filling up, it's filling up, it's full.
And there it is.
Hurray! APPLAUSE Isn't that satisfactory? Highly satisfactory.
It's the first theorem most people learn at school.
It's Pythagoras's theorem by name, but it wasn't, it was used many, many years before him - people used it to build buildings and Euclid demonstrated it before him.
But we give it the name of Pythagoras.
Who is Euclid, then? He was even before? He's the father of mathematics.
Euclid? - Oh, was he? - Yeah.
- Yeah.
- Oh, Euclid, yes.
Before him, nothing.
The greatest.
Yeah, well done to Euclid, we love Euclid.
So, let's take this model away.
Let's hear it for him.
APPLAUSE So, the time has come to tally-up the scores.
Oh, my actual, oh, my actual.
So, in first place, with a magnificent two points, it's Aisling Bee! Oh! APPLAUSE And with an earth-shattering zero, it's Sandi Toksvig.
APPLAUSE A more than respectable minus six, Susan Calman.
APPLAUSE And on his terms, really quite handsome, minus 43, Alan Davies.
APPLAUSE So, it's goodnight from Susan, Sandi, Aisling, Alan and me.
And I'll leave you with this dark observation from Joseph Stalin.
My favourite dictator.
"The people who cast the votes decide nothing.
"The people who count the votes decide everything.
" Goodnight.
CHEERING AND APPLAUSE